Geometry & Topology Volume 20, issue 4 (2016)

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Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces

Vincent Humilière, Frédéric Le Roux and Sobhan Seyfaddini

Geometry & Topology 20 (2016) 2253–2334

DOI: 10.2140/gt.2016.20.2253

Bibliography

1	M Audin, M Damian, Morse theory and Floer homology, Springer (2014) MR3155456
2	B Bramham, Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves, Ann. of Math. 181 (2015) 1033 MR3296820
3	B Bramham, Pseudo-rotations with sufficiently Liouvillean rotation number are C⁰–rigid, Invent. Math. 199 (2015) 561 MR3302121
4	M Brunella, On a theorem of Sikorav, Enseign. Math. 37 (1991) 83 MR1115746
5	D N Dore, A D Hanlon, Area preserving maps on S² : a lower bound on the C⁰–norm using symplectic spectral invariants, Electron. Res. Announc. Math. Sci. 20 (2013) 97 MR3268419
6	M Entov, Quasi-morphisms and quasi-states in symplectic topology, preprint (2014) arXiv:1404.6408
7	M Entov, L Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. 2003 (2003) 1635 MR1979584
8	M Entov, L Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv. 81 (2006) 75 MR2208798
9	M Entov, L Polterovich, Rigid subsets of symplectic manifolds, Compos. Math. 145 (2009) 773 MR2507748
10	A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775 MR948771
11	A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
12	U Frauenfelder, F Schlenk, Hamiltonian dynamics on convex symplectic manifolds, Israel J. Math. 159 (2007) 1 MR2342472
13	V L Ginzburg, The Conley conjecture, Ann. of Math. 172 (2010) 1127 MR2680488
14	V L Ginzburg, B Z Gürel, Local Floer homology and the action gap, J. Symplectic Geom. 8 (2010) 323 MR2684510
15	A Gramain, Le type d’homotopie du groupe des difféomorphismes d’une surface compacte, Ann. Sci. École Norm. Sup. 6 (1973) 53 MR0326773
16	M Handel, Commuting homeomorphisms of S², Topology 31 (1992) 293 MR1167171
17	D Hein, The Conley conjecture for irrational symplectic manifolds, J. Symplectic Geom. 10 (2012) 183 MR2926994
18	M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
19	V Humilière, R Leclercq, S Seyfaddini, New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians, Comment. Math. Helv. 90 (2015) 1 MR3317330
20	O Jaulent, Existence d’un feuilletage positivement transverse à un homéomorphisme de surface, Ann. Inst. Fourier (Grenoble) 64 (2014) 1441 MR3329669
21	A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
22	M Kawasaki, Superheavy Lagrangian immersion in 2-torus, preprint (2016) arXiv:1412.4495
23	S Lanzat, Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds, Int. Math. Res. Not. 2013 (2013) 5321 MR3142258
24	P Le Calvez, Propriétés dynamiques des difféomorphismes de l’anneau et du tore, 204, Société Mathématique de France (1991) 131 MR1183304
25	P Le Calvez, Une version feuilletée équivariante du théorème de translation de Brouwer, Publ. Math. Inst. Hautes Études Sci. 102 (2005) 1 MR2217051
26	P Le Calvez, A finite dimensional approach to Bramham’s approximation theorem, preprint (2013) arXiv:1307.5278
27	E L Lima, On the local triviality of the restriction map for embeddings, Comment. Math. Helv. 38 (1964) 163 MR0161343
28	D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
29	Y G Oh, Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, from: "The breadth of symplectic and Poisson geometry" (editors J Marsden, T Ratiu), Progr. Math. 232, Birkhäuser (2005) 525 MR2103018
30	Y G Oh, Lectures on Floer theory and spectral invariants of Hamiltonian flows, from: "Morse theoretic methods in nonlinear analysis and in symplectic topology" (editors P Biran, O Cornea, F Lalonde), NATO Sci. Ser. II Math. Phys. Chem. 217, Springer (2006) 321 MR2276955
31	S Piunikhin, D Salamon, M Schwarz, Symplectic Floer–Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
32	L Polterovich, The geometry of the group of symplectic diffeomorphisms, Birkhäuser (2001) MR1826128
33	L Polterovich, Symplectic geometry of quantum noise, Comm. Math. Phys. 327 (2014) 481 MR3183407
34	L Polterovich, K F Siburg, On the asymptotic geometry of area-preserving maps, Math. Res. Lett. 7 (2000) 233 MR1764319
35	P Py, Quasi-morphisme de Calabi sur les surfaces de genre supérieur, C. R. Math. Acad. Sci. Paris 341 (2005) 29 MR2153388
36	P Py, Quasi-morphismes de Calabi et graphe de Reeb sur le tore, C. R. Math. Acad. Sci. Paris 343 (2006) 323 MR2253051
37	M Rosenberg, Py–Calabi quasi-morphisms and quasi-states on orientable surfaces of higher genus, Israel J. Math. 180 (2010) 163 MR2735061
38	D Salamon, Lectures on Floer homology, from: "Symplectic geometry and topology" (editors Y Eliashberg, L Traynor), IAS/Park City Math. Ser. 7, Amer. Math. Soc. (1999) 143 MR1702944
39	D Salamon, E Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303 MR1181727
40	M Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000) 419 MR1755825
41	S Seyfaddini, The displaced disks problem via symplectic topology, C. R. Math. Acad. Sci. Paris 351 (2013) 841 MR3128973
42	S Seyfaddini, Spectral killers and Poisson bracket invariants, J. Mod. Dyn. 9 (2015) 51 MR3395260
43	J C Sikorav, Sur les immersions lagrangiennes dans un fibré cotangent admettant une phase génératrice globale, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986) 119 MR830282
44	D Théret, A complete proof of Viterbo’s uniqueness theorem on generating functions, Topology Appl. 96 (1999) 249 MR1709692
45	M Usher, Floer homology in disk bundles and symplectically twisted geodesic flows, J. Mod. Dyn. 3 (2009) 61 MR2481333
46	C Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685 MR1157321
47	F Zapolsky, Isotopy-invariant topological measures on closed orientable surfaces of higher genus, Math. Z. 270 (2012) 133 MR2875825
48	F Zapolsky, Reeb graph and quasi-states on the two-dimensional torus, Israel J. Math. 188 (2012) 111 MR2897725